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Today's calculation of Integral 718

Source: 1989 The University of Electro-Communications　entrance exam

June 26, 2011
calculusintegrationcalculus computations

Problem Statement

Find ∑n=1∞12n∫−11(1−x)2(1+x)ndx (n≥1).\sum_{n=1}^{\infty} \frac{1}{2^n}\int_{-1}^1 (1-x)^2(1+x)^n dx\ (n\geq 1).
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